Yeah, this kind of thing can be tricky. First off, are we sure your car's stereo is bluetooth-enabled? You'll have to confirm that of course.
it's possible that your two devices might not share the right bluetooth profile due to the age of your car.
I've heard about one trick you might try. First, do the connect like you did before. Then, make a call on your phone, say to your own voicemail. After the call connects, ,and while it is still connected, shut off the phone connection on your car's audio system, ,and then re-connect and try to pair again ( keeping your phone on the whole time).
You may need to contact the car stereo's manufacturer to figure this out.